# Definition:Euclid's Definitions - Book X/4 - Rational Area

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## Definition

In the words of Euclid:

*And let the square on the assigned straight line be called***rational**and those areas which are commensurable with it**rational**, but those which are incommensurable with it**irrational**, and the straight lines which produce them**irrational**, that is, in case the areas are squares, the sides themselves, but in case they are any other rectilineal figures, the straight lines on which are described squares equal to them.

(*The Elements*: Book $\text{X}$: Definition $4$)

## Sources

- 1926: Sir Thomas L. Heath:
*Euclid: The Thirteen Books of The Elements: Volume 3*(2nd ed.) ... (previous) ... (next): Book $\text{X}$. Definitions